In this paper, we present some new (in-)tractability results related to the integration problem in subspaces of the Wiener algebra over the $d$-dimensional unit cube. We show that intractability holds for multivariate integration in the standard Wiener algebra in the deterministic setting, in contrast to polynomial tractability in an unweighted subspace of the Wiener algebra recently shown by Goda (2023). Moreover, we prove that multivariate integration in the subspace of the Wiener algebra introduced by Goda is strongly polynomially tractable if we switch to the randomized setting. We also identify subspaces in which multivariate integration in the deterministic setting are (strongly) polynomially tractable and we compare these results with the bound which can be obtained via Hoeffding's inequality.

翻译：本文针对$d$维单位立方体上维纳代数子空间中的积分问题，提出了一些新的（不可）可处理性结果。我们证明了在确定性设定下，标准维纳代数中的多元积分具有不可处理性，这与Goda（2023）最近在维纳代数的无权重子空间中证明的多项式可处理性形成对比。此外，我们证明若转向随机化设定，则Goda所引入的维纳代数子空间中的多元积分具有强多项式可处理性。我们还识别出在确定性设定下多元积分具有（强）多项式可处理性的子空间，并将这些结果与通过Hoeffding不等式所能获得的界进行了比较。